Preheat your oven to 465°F (240°C). Line a baking sheet with parchment paper and position two ungreased 7-inch pastry rings on top.

In a food processor, pulse together the shelled pistachios, powdered sugar, and cake flour until finely combined. Set aside.

Beat the egg whites until foamy. Gradually add cream of tartar and salt, then slowly incorporate granulated sugar while continuing to whip until stiff peaks form.

Gently fold the pistachio mixture into the meringue in two additions, being careful not to deflate the egg whites.

Spoon the meringue mixture into the pastry rings on the prepared baking sheet. Reduce oven to 350°F (180°C) and bake for 15 minutes. Then let cool in the oven with the door ajar.

In a bowl, beat the egg yolks until pale. In a saucepan, combine sugar and water, cooking until it reaches 240°F. Slowly pour into the yolks while mixing, then gradually add softened butter and finish by stirring in vanilla, pistachio paste, and salt.

Assemble the cake by placing one dacquoise layer on a serving plate, piping buttercream around the edge, filling the center, topping with the second layer, and decorating.